1. Field of the Invention
The present invention relates specifically to anew seismic attribute for seismic trace analysis.
More specifically, the present invention relates to application of a wavelet transform to seismic traces and subsequent calculation of pointewise Hxc3x6lder exponents at local time points. The resulting data can be used to produce greatly improved seismic imaging of stratigraphic features in 2D, 3D or time lapse data. The Hxc3x6lder exponents correlate closely with results from acoustic impedance and therefore allow data gathering to provide new geophysical information. In addition, Hxc3x6lder exponents calculated from singularities in the traces very sharply and distinctly delineate borders between strata.
2. Prior Art
In the petroleum industry, drilling risk is best reduced by accurate, reliable imaging of geological subsurface formations. Stratigraphic and geophysical data is vital to finding petroleum reservoirs. A rapidly expanding area of oil exploration is in the image analysis of seismic trace data.
In order to obtain a view of the subsurface geology, explorationists generate seismic waves and use sensors to detect reflections of these waves. Interfaces in the subsurface strata reflect these waves. By measuring the returned amplitude and the time between initiation of the wave and its reflection to the surface, subsurface features may be detected. Measurements made by the sensors are known as seismic traces.
A variety of methods have been developed to reduce noise and increase resolution. Traces resulting from identical points in the subsurface may be stacked (summed) and migrated. This both reduces noise and increases resolution. However, coherent noise tends to be amplified by trace stacking. Fourier transforms may also be applied to seismic traces in an effort to identify and eliminate coherent noise. There have been many attempts to improve interpretation of seismic trace data, none of which contemplate the methodology of the present invention.
The patent (U.S. Pat. No. 5,563,949) to Bahorich et al. (1996) and the patent (U.S. Pat. No. 6,092,025) to Neff(2000) fall into the category of a new seismic attribute from seismic data. The attribute from U.S. Pat. No. 5,563,949, coherency cube, is from similarity or correlation analysis of adjacent seismic traces and gives better standout of geological structures such as faults or edges of salt domes. However, the nature of their algorithm makes their attribute useful primarily only on horizontal or time slices and all relevant stratigraphic information on vertical sections are smeared out. There is no application of a wavelet transform.
U.S. Pat. No. 6,092,025 calculates a type of seismic attribute called Delta Amplitude Dip (DAD), also based on similarity or cross-correlation analysis of adjacent seismic traces, and claims that displaying DAD values in a time or horizontal slice provides a direct indicator of hydrocarbon. Cross-correlation analysis is good for edge detection, and thus both coherency cube and DAD are suitable for detecting faults or edges in seismic data. At the same time they also share the same kind of drawbacks (DAD attribute is also only suitable for time or horizontal slice). In contrast, the algorithm of the present invention, based on the wavelet transform, is highly localized and gives clearer images of subsurface singularity variations, and therefore is able to deliver stratigraphic and structural information from both vertical and horizontal sections.
One important feature of the present invention is the application of wavelet transform and the calculation of Hxc3x6lder exponent/singularity analysis on seismic data. None of these operations or analyses was performed in reported patents. However, the algorithm named very short-time Fourier transform (VSTFT), in the invention (U.S. Pat. No. 5,850,622) of Vassiliou et al., (1998) is similar to ours. Vassiliou et al. claimed that by using VSTFT, shorter in length than was felt to be possible, they discovered a novel method of reorganizing the data in frequency domain so that noise can be better removed or attenuated, and attribute analysis and trance editing becomes easier. Their method gives no clue as to how singularity analysis can be performed.
As we all know, wavelet transform is an outgrowth of Fourier transform or short-time Fourier transform, but what makes the wavelet transform more powerful is that it is localized in both frequency and time domain. The Short-time Fourier transform tries to gain some time resolution with a short, fixed-length time window. Unlike the wavelet transform which uses variable-length windows, a fixed window will make the time resolution everywhere the same. According to the Reciprocal Uncertainty Principle, a very short time window, as implemented by Vassiliou et al., gives better time resolution but poor frequency resolution, which makes localized frequency analysis very impractical.
Several inventions (U.S. Pat. No. 4,679,174 to Gelfand; U.S. Pat. No. 4, 817,062 to De Buyl et al.; U.S. Pat. No. 5,487,001 and U.S. Pat. No. 6,092,025 to Neff) are focused on combining geologic information, such as well logs, with seismic data for extracting subsurface lithologic information. These generally involve modeling and inversion. These inventions are unlike the present invention in terms of research goal and methodology. U.S. Pat. No. 4,679,174 (Gelfand) basically explores the power of forward modeling and iteratively compares seismic synthetics with real seismic data until an acceptable match has been achieved. Gelfand attempts to use modeling to recover high-frequency components in the seismic spectrum that are lost during seismic exploration. The present invention does not try to recover high-frequency components (fine scale stratigraphic information) lost in the seismic trace. Rather, it focuses on delineating locations and singularity strengths of stratigraphic boundaries. The present invention creates an image showing a new attribute in which stratigraphic information is more prominent than in seismic amplitude images (where the nature of seismic reflectivity can obscure true acoustic impedance variations). Even though seismic data are band-limited, the amplitude spectrum for a typical seismic trace still reveals a frequency band of xcx9c10 to 100 Hz, which is broad enough for a successful multiscale analysis based on continuous wavelet transform. Since no inverse wavelet transform is necessary for singularity analysis, the invention disclosed herein simply analyzes the scaling information within the seismic frequency band.
U.S. Pat. No. 4,817,062 (De Buyl et al., 1989) applies similar data sets and concepts as U.S. Pat. No. 4,679,174 (Gelfand). In U.S. Pat. No. 4,817,062 a method for estimating subsurface porosity is established based on integration of well and seismic data. First, a seismic acoustic model is obtained from seismic survey. Then porosity information is assessed based on a porosity-acoustic impedance relationship they derived in the invention. Both the goal and the methodology of De Buyl et al. are quite different from ours.
Two patents to Neff (U.S. Pat. No. 5,487,001 and U.S. Pat. No. 6,092,025) disclose estimating subsurface petrophysical properties from the integration of seismic and well data. They are very similar in concept, both applying forward modeling, synthetic generation, iterative comparison between synthetics and real seismic traces. U.S. Pat. No. 5,487,001 (1996) is designed to determine petrophysical properties associated with a subterranean layer, while patent U.S. Pat. No. 6,092,025 (1998) is more tuned for estimating vertical permeability and porosity variations within a reservoir. Neither utilizes the wavelet transform and thus distinct from the present invention.
The patent (U.S. Pat. No. 6,246,963 B1) to Cross et al. (2001) involves no seismic data but quantitative stratigraphic modeling to predict stratigraphic and sedimentologic attributes at locations other than those at which data are collected. Clearly this invention falls into the category of mathematical modeling in geology and geostatistics, and does not bear any similarity to the present invention.
Alam""s invention (U.S. Pat. No. 6,278,949) is a method for multiple attribute identification of structure and stratigraphy in a volume of seismic data. First, multiple attributes are generated from seismic data, and then subsets of multiple attributes are interactively selected, thresholded and combined with one of a suite of mathematical operators into a scalar function. By manipulating the attribute volume, a user visually recognizes bodies of potential hydrocarbon reservoirs on a color graphic workstation. This invention focuses on the manipulation of different attributes but gives no indication how to generate these attributes. Alam""s invention does not disclose computation of the Hxc3x6lder exponent or its use in subsurface imaging. The computation of the Hxc3x6lder exponent from seismic data is an important component of the present invention.
Seismic processing can be subdivided into two categories, data processing and image processing, based on the type of data input to the processing and on the purpose of the processing. Data processing includes all the processing steps that are aimed at obtaining a final subsurface image based on seismic amplitudes. These steps include deconvolution, NMOIDMO, migration, etc. Image processing is aimed at extracting further geological information from the migrated seismic data. A key distinction is that data processing algorithms typically exploit aspects of seismic wave propagation, whereas image processing tends to be more geared, and would be equally applicable, to non-seismic data problems. For example, coherency and instantaneous attributes would fall in the image processing category. Image processing products are commonly termed xe2x80x9cattributesxe2x80x9d in seismic work. With an ever-increasing need to extract geological information from seismic data, image processing becomes more and more important.
Seismic amplitude plays the predominant role in seismic interpretation and is the raw material for image processing. While it is critically important, it can also disguise true geological features from the unaided eye. It would be very informative to have a type of attribute that is independent of seismic amplitudes but also geologically sharp and meaningful on a cross section. Among some of the most frequently applied seismic attributes, AVO (amplitude versus offset) is based on prestack data and is limited to certain targets, coherency is good generally for time slice interpretations but destroys information on vertical sections, and instantaneous phase or instantaneous frequency are unable to localize in time to indicate sharp stratigraphic boundaries. Thus there is an ongoing need for additional ways to extract stratigraphic information directly from seismic amplitude volumes.
It is therefor desirable to provide improved seismic visibility of stratigraphic features and additional geologic information from existing seismic trace data
It is also desirable to provide a method of interpreting seismic trace data that does not depend upon seismic amplitude.
In the present invention the Hxc3x6lder exponent (xcex1) is introduced as a new seismic attribute capable of capturing irregularities in seismic data xcex1 measures the regularity of seismic trace data by measuring the growth or decay of wavelet coefficients across a range of scales for each time point in the data. Herein the term scale is taken to be synonymous with frequency. Those skilled in the art will appreciate that there are other, similar methods of measuring the regularity of the data, such as the VSTFT and the Hurst exponent. However, xcex1 provides the most accurate and reliable attribute for elucidating stratigraphic information in geophysical data.
Seismic interpretation has been traditionally based on seismic reflectivity strengths measured by amplitude. However, studying amplitude alone can disguise the true nature of subsurface geology and produce blurred stratigraphic boundaries. Very often important information is found in singularities that are not necessarily associated with a certain amplitude pattern. xcex1 is a measure of singularity strength defined at or around a point. The more regular the data, the larger the value of xcex1.
The Hxc3x6lder exponent is computed using wavelet-based multiscale analysis, which is the preferred tool in detecting both the location of the singularity strengths and sharp changes in the signal. xcex1 improves our ability to delineate stratigraphic layer boundaries that are vague in the original amplitude based seismic images. The natural attribute xcex1 provides a major breakthrough in how seismic data are interpreted.
This new attribute xcex1 is derived from seismic trace data to provide a new image processing product. It provides for cleaner images of stratigraphic boundaries and features. There is nothing in the prior art that would suggest that application of a wavelet transform and subsequent measurement of growth/decay along a range of scales would have any beneficial results, much less the improved detection of stratigraphic boundaries and additional geophysical information provided by the present invention.
According to the present invention, seismic trace data, expressed as amplitude versus time, is subjected to a wavelet transform which converts the data into a two dimensional graph in which the wavelet coefficient parameter is a function of time and scale. Wavelet transforms have the advantage of high resolution in both time and scale. In comparison, VSTFT is highly resolved in either time or frequency, but not both. In wavelet transform literature this is referred to as the Heisenberg uncertainty principle. This makes VSTFT and other transforms that are subject to the Heisenberg uncertainty principal undesirable in the present invention. This resolution trade off prevents them from producing the high resolution, informative results of the present invention.
Once the seismic trace has been transformed, further studies can be made at individual time points. This results in a series of two dimensional graphs of wavelet coefficient versus scale for each localized time point. When these two parameters are expressed on a log-log plot, they exhibit a linear relationship. Any of a number of linear regression methods may be utilized in order to determine the wavelet coefficient/scale slope of this line. A least-squares linear regression is a well-known, preferred method of determining such a slope. This slope is known as a Hxc3x6lder Exponent (xcex1). Of course, the Hxc3x6lder exponent may be derived from non-log plots, but the calculations are significantly more cumbersome.
Hxc3x6lder exponents are calculated for each localized time point of a seismic trace. This provides the Hxc3x6lder exponent as a function of time, referred to herein as a Hxc3x6lder trace. These Hxc3x6lder traces are displayed in place of seismic traces to create a Hxc3x6lder image, volume or time-lapse volume. The resulting Hxc3x6der image has the property that geophysical and stratigraphic characteristics that are not readily apparent in typical reflectivity image graphs are easily observed in a Hxc3x6lder trace image. Geologic features that are blurred and/or very difficult or impossible to identify in standard seismic trace reflectivity imaging graphs become apparent in the maps produced by Hxc3x6lder exponents.
The Hxc3x6lder exponent is a measure of asymptotic behavior of the wavelet coefficient versus scale. Nothing in the prior art suggests that the asymptotic behavior of wavelet coefficients across a range of scales would elucidate any seismologic, stratigraphic, geophysical or lithologic information from a seismic trace. In fact, the prior art, such as the patent to Vassiliou, actually teach away from measuring wavelet coefficient behavior across a scale or range and state that the frequency range is too narrow for such an analysis. One of the unexpected features of the present invention is the discovery of a method for accurately analyzing singularities at a localized point in time by choosing an appropriate range of scales in order to minimize the standard deviation of a linear regression. Another novel, unforeseen aspect of the present invention is that by analyzing asymptotic behavior of singularities using a wavelet-based method will both optimize the resolution of seismic imaging and provide additional geophysical data. Another surprising result of this method of singularity analysis is that it correlates well with results from acoustic impedance data. This provides even more geophysical and lithologic information.